%I A002309 M5359 N2327
%S A002309 1,82,707,3108,9669,24310,52871,103496,187017,317338,511819,791660,1182285,
%T A002309 1713726,2421007,3344528,4530449,6031074,7905235,10218676,13044437,16463238,
%U A002309 20563863,25443544,31208345,37973546,45864027,55014652,65570653,77688014
%N A002309 Sum of fourth powers of odd numbers.
%D A002309 J. L. Bailey, Jr., A table to facilitate the fitting of certain logistic 
               curves, Annals Math. Stat., 2 (1931), 355-359.
%D A002309 F. E. Croxton and D. J. Cowden, Applied General Statistics. 2nd ed., 
               Prentice-Hall, Englewood Cliffs, NJ, 1955, p. 742.
%D A002309 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002309 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002309 T. D. Noe, <a href="b002309.txt">Table of n, a(n) for n=1..1000</a>
%H A002309 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A002309 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A002309 a(n)=(48*n^5-40*n^3+7*n)/15. - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               Jan 29 2003
%p A002309 A002309:=(1+76*z+230*z**2+76*z**3+z**4)/(z-1)**6; [Conjectured by S. 
               Plouffe in his 1992 dissertation.]
%t A002309 Table[(48*n^5 - 40*n^3 + 7*n)/15, {n, 0, 40}] - Stefan Steinerberger 
               (stefan.steinerberger(AT)gmail.com), Apr 10 2006
%t A002309 s = 0; lst = {s}; Do[s += n^4; AppendTo[lst, s], {n, 1, 60, 2}]; lst 
               [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
%Y A002309 Cf. A002593.
%Y A002309 Sequence in context: A005972 A082972 A031422 this_sequence A128959 A160914 
               A083386
%Y A002309 Adjacent sequences: A002306 A002307 A002308 this_sequence A002310 A002311 
               A002312
%K A002309 nonn,nice
%O A002309 1,2
%A A002309 N. J. A. Sloane (njas(AT)research.att.com).